In this research, a parametric investigation of irreversible Stirling heat pump cycles that includes both internal and external irreversibilities together finite heat capacities of external reservoirs is carried out. Finite temperature difference between the external fluids and the working fluids through the heat sink and heat source causes an external irreversibility. On the other hand, regenerative heat loss and entropy generation through the cycle are the main source of the internal irreversibilities generation. Three objective functions including the heating load (RH) and coefficient of performance (COP) and thermo-economic criterion (F) have been considered simultaneously maximized. To evaluate this goal, Multi-objective optimization method jointed to NSGA-II approach is implemented, which following parameters are included as decision parameters such as 1 – the effectiveness of the hot-side heat exchanger, 2 – the effectiveness of the cold-side heat exchanger, 3 – the rate of heat capacitance through the heat sink and heat source, 4 – temperature ratio T h T c , and 5 – temperature of cold side. By accomplishing above mentioned multi-objective optimization method, Pareto optimum frontier figured out, and with the aim of well-known decision-makers which consists the LINMAP, \FUZZY\ Bellman-Zadeh and \TOPSIS\ techniques, final optimum answers are specified.